146 3Ir. Lubbock oh the Calculation of Annuities, and 



This probability is the same as if the simple probability of drawing 

 a ball of the />"" colour were m^ + l, with the difference of notation. 



When Ws, n^, rip-x, &c. = 0, and n^ = 1, this expression gives 

 for the chance of drawing a ball of the p"" colour, 



mp+ \ 



mi + m.,. . . . +mi'+p' 



and the probability that the index of the colour drawn is between 



n - 1 and ii + (j + i is 



wjj + 7«o . . . . +mp +p 



If we suppose the law of the possibility of life to be such that 

 p cases or ages are possible, a priori, »«i, m„, &c. will be the 

 number of recorded deaths in a table of mortality at those re- 

 spective ages, and the chance of an individual living beyond the 

 m"' age will be 



m„ + m„^-^ .... nip+p-n 

 /Mi + 7?jj +mp + p ' 



m„ + m„_i + ikc.+mp is the number given by the table as living at 

 the n* year ; therefore, on the hypothesis of this law of possibility, 

 the chance of an individual living beyond the n'" year is a fraction 

 of which the numerator is the number living at that age +p-n, 

 and the denominator is the whole population on which the table 

 is founded, or the radix + /'. The tables 1 and 2 have been 

 calculated from this formula from observations at Chester, given by 

 Dr. Price, Vol. II. p. 107. ; p was taken equal to 101 for a child 

 at birth, that is, the chances of a child living beyond a hundred 

 years, and of its dying in each intermediate year, were supposed 

 to vary from to 1, all these values being equally probable, 

 a priori. The value of any sum to be received after any number 

 of years is equal to the sum itself multiplied by the chance of 



